Basement remodel, help with an efficient layout? (diagram incl.)

I have a split-level/split-entry/split-foyer house, whatever it's called in your part of the country. My basement is largely unfinished, except for a couple of walls the previous owners haphazardly put up, which will be ripped down when this remodel starts. Everything will be ripped out back to the cinder block so I can check for any potential issues, frame & insulate it properly, and get any electrical and media cabling where it needs to go.

Currently, the top left room is finished enough to be habitable. Painted drywall, carpet. Unfortunately due to the lally column under the header, there is a small wall there to conceal it. If I could open that up completely that would be ideal.

The top right room we planned on making into a playroom for my kids (1 & 3). You can see because of the support columns, it would make most sense to wall all the way across that.

The rest of the basement, can be broken up however you see fit. Prefer to keep the washer/dryer/water pump in that general area, but, we can move things around in there, not a big deal. All the plumbing and electric is exposed and easy to move.

Because of the HVAC supply/return and the header, I'm going to need a soffit of some type built around it, so I will be losing some ceiling height there.

Thinking that a half-bath would be good to put in also. Just to the left of the laundry room wall, against the bottom wall, is some rough plumbing.

Anyways, looking for ideas here. Thanks in advance.

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Basement remodel, help with an efficient layout? (diagram incl.)

This was one idea. Make a closet accessible from the top room to store extra clothing (military, lots of extra stuff), as well as a place to swap winter/summer stuff etc. House is very short on closet space.

Then, have laundry room access from the play room. Good time to do laundry. Put a half bath on the other side of the wall.